The fine-grained uncertainty relation can be used to discriminate among classical, quantum, and superquantum correlations based on their strength of nonlocality, as has been shown for bipartite and tripartite systems with unbiased measurement settings. Here we consider the situations when two and three parties choose settings with bias for playing certain nonlocal games. We show analytically that while the fine-grained uncertainty principle is still able to distinguish classical, quantum, and superquantum correlations for biased settings corresponding to certain ranges of the biasing parameters, the above-mentioned discrimination is not manifested for all biasing.
Can uncomputability occur in the resource law of one fixed finite nonlocal game, rather than in a problem whose input is a game? We construct a finite two-player Boolean constraint-system game with rational question probabilities, quantum value one, and no finite-dimensional perfect strategy. If
D(ε) is the least local dimension needed to win with probability at least
1−ε, then
limn→∞log2D(2−n)/n=(3+θK)/4, where
θK=∑e∈K4−(e+1) and
K is the halting set. This exponent has the Turing degree of
K. The construction combines finite operator relations for three Cantor clocks, a counter program with forced initialization, and a conditional clock that charges dimension for halting inputs. A Boolean compiler preserves weighted precision linearly and converts flat models to strategies with quadratic loss. The lower bound holds in every density matrix. Explicit finite models attain the same rate. The flag-density lower bound uses compactness without an effective modulus; convergence to the dimension exponent has no computable certified rate.